الفهرس 
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Abstract
This chapter outlines a brief summary of the current research. The main conclusions together with recommendations for future studies are also presented.
A comprehensive literature review is done to cover all the aspects of research that deals with the hollow flange girders. It was found that the main issue that limits the use of such kind of girders is the lateral torsional buckling. The bending capacity of the girder is limited to LTB. Therefore, the main aim of this research is to improve the performance of HTFG against all modes of failure by enhancing the geometric configuration of the HTFG to reduce the effect of LTB that sections suffers from.
A finite element model is developed using ABAQUS finite element package to investigate the flexural behavior and moment capacities of simply supported HTFG. Many factors are taken into account when modelling the HTFG such as material and geometric nonlinearities as well as the geometric imperfections.
The proposed FEM is validated against published experimental results found in the literature and showed a very good agreement in terms of the ultimate moment as well as the load-deformation behavior. Therefore, the model is considered to be accurate enough to predict the bending behavior of the HTFG.
Same factors considered in the validated model are considered in the models used in the parametric study but with ideal conditions as follows:
- The girder is simply supported.
- An end moment at supports is adopted to produce a pure moment condition.
- Load applied as line load at compression and tension sides to avoid any stress concentration at any points on flange.
- Mesh size is 50mm.
A comprehensive parametric study is conducted to investigate the best geometric configuration for the HTFG to improve its flexural strength. The idealized boundary conditions are considered the most critical case for the development of moment capacity design rules.
The research focused on studying the effect of classes of flange and web. All classes of flange and web are studied (Compact, Non-compact and Slender) sections -according to AISC and (Class 1, 2, 3 and 4) in EN. multiple hollow flange dimensions 200, 300 and 400mm for width and depth of flange are also used in this research. Different flange depths are also studied with constant CL. to CL. value of 1400mm. depths of flange ranges from 400mm to 0mm-as plate girder. Ten different spans of 2000, 3000, 5000, 10000, 15000, 20000, 30000, 40000, 50000 and 60000mm are considered as short, intermediate and large spans to cover all modes of failure (LB, LTB and LDB).
The main studied geometric parameters are the classifications of flange and web. All 3 different classes in AISC and 4 classes in EN are discussed to study the effect of flange and web classifications on the flexural strength of HTFGs. It is found that this parameter has a great effect on the behavior of HTFGs, where changing class of web has significant effect especially the S web which cause low capacity.
Another parameter is the aspect ratio of the hollow flange and depth ratio of the girder to its width (2 to 0.5). Nine different specimens are studied with flange and web dimensions ranges (200, 300, and 400) mm. It is also found that area of flanges has major effect on HTFG flexural capacity, where by increasing area of flange the capacity of HTFG increases, also flanges with same area such as (400x200 & 200x400) has almost same capacity.
It is found that the two above parameters have a great effect on the behavior of the HTFG for all the studied specimens, and by using the right configuration we can dramatically improve the girder flexural strength against all modes of failure specially LTB.
Also, the current design rules available in AISC are reviewed with the FEM results and it is found very conservative in slender web due to neglecting the section torsion constant, while it is unconservative for the non-compact web. A modification is proposed to modify the current design rules to accurately predict the bending capacity of the HTFG with different geometric configurations. The approaches of the modification are presented then applied in a new equation proposed in this research.
Another parametric study conducted is the flange depth. Variable flange depths are studied (400, 300, 200, 100, PG) mm. it can be seen that by increasing the flange depth the capacity of HTFG starts to increase. It is applicable for different girder spans.
Also, another parametric study is the girder span. Different girder lengths are conducted (2000, 2000, 3000, 5000, 10000, 15000, 20000, 30000, 40000, 50000 and 60000) mm are conducted to study the effect of span girder over the flexural capacity of HTFG. Variable lengths are chosen as short, intermediate and large spans to cover all modes of failure (LB, LTB and LDB). It was found that by increasing the span girder the capacity of HTFG starts to decrease, with big DROP especially in S web. It could be noticed that when it comes to intermediate spans (15m) there is a big reduction of capacity due to the appearance of LTB.
5.2 Conclusions
Based on the numerical results of the HTFGs with different geometric configurations as well as the results obtained by the comparison with the other I-beams, the following conclusions may be deduced:
1- Changing class of tubular flange from C to N to S has minor effect on the flexural strength of the HTFG, while the web class has significant effect especially the S web which cause low capacity.
2- For the yielding failure mode of HTFG with C web and C flange, the plastic section modulus is limited to 10% increasing of the elastic section modulus. Full plastification of the section is not likely occurred.
3- For HTFG with S web and long spans, applying J = 0 in the LTB formula gives an excessive conservative estimate of the flexural strength. J need not be ignored in HTFG, at the same time it cannot be taken with its full value. where a better estimate of the LTB resistance is needed, a potential proposal to calculate the elastic LTB using J with a percentage as a function of Lb/rt is developed.
4- For HTFG with N web, the LTB formula gives an overestimated value of the flexural strength. J of the tubular flanges needs to be reduced. A potential proposal to calculate the elastic LTB using J with a percentage function of Lb/rt is developed.
5- For HTFG with same area of flange gives almost same capacity of girder, which mean the area of flange has major effect on flexural strength of girder.
6- By increasing flange depth of HTFG, flexural capacity of girder increases gradually depending on flange and web classes. For compact flange and compact web with 400mm flange depth it reaches over yielding moment by 15%.
7- For HTFG with length 15m and above, the effect of LTB starts to present obviously. Small lengths as 2m, 3m and 5m the effect of LB is the major mode of failure.
5.3 Recommendations for future work
1- Apply experimental models simulating the studied case.
2- Study the effect of geometric configurations under different moment distributions.
3- Study the effect of transverse stiffeners over the HTFGs.
4- Study the effect of full depth web going throw the flange.
5- Takes into account the shear buckling when studying the recommended depth of web depth-to-plate width ratio